sin-x-1-x-0-05-0-1-

Question Number 56647 by ANTARES VY last updated on 20/Mar/19

$$\boldsymbol{\mathrm{sin}}\left(\frac{\boldsymbol{\pi}}{\boldsymbol{\mathrm{x}}}\right)=\mathrm{1} \\ $$$$\boldsymbol{\mathrm{x}}\in\left[\mathrm{0}.\mathrm{05};\mathrm{0}.\mathrm{1}\right] \\ $$

Commented by ajfour last updated on 20/Mar/19

$$\mathrm{sin}\:\left(\frac{\pi}{\mathrm{x}}\right)=\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}+\mathrm{2k}\pi\right) \\ $$$$\mathrm{k}\in\left\{\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9}\right\} \\ $$$$\Rightarrow\:\:\mathrm{x}=\frac{\mathrm{2}}{\mathrm{4k}+\mathrm{1}}\:=\:\left\{\frac{\mathrm{2}}{\mathrm{21}},\frac{\mathrm{2}}{\mathrm{25}},\frac{\mathrm{2}}{\mathrm{29}},\frac{\mathrm{2}}{\mathrm{33}},\frac{\mathrm{2}}{\mathrm{37}}\right\} \\ $$

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